This audio frequency meter uses 555 IC as a monostable multivibrator (one-shoot trigger). A monostable multivibrator can act as a frequency-to-voltage converter because it produce a fixed pulse width, with the repetition rate/density is proportional to the triggering input frequency. Here is the circuit’s schematic diagram:

audio frequency meter 555 circuit schematic

For resistor R1, because it set the measurement range, it’s better to use a rotary switch to select different values for different ranges. For the ampere meter, you can use both analog or digital ampere meter. A cheap dual-slope ADC digital meter is suitable because its averaging characteristic, but a fast digital multimeter can also be used although it may show some uncertainty because of their fast sampling.